A blog on the nature of things.
Created by the Centre for Metaphysics and Mind (CMM). Leeds, UK.

Friday, January 29, 2010

Truthmaking and In Virtue Of

Suppose you believe in both truthmaking and metaphysical dependence. That is, you believe both that for some true proposition p there is some thing or things which make p true, and that for some true propositions q and r, q is true in virtue of r. Neither relationship, you think, is to be analysed modally: the truth of ‘Necessarily, if A exists then p’ is a necessary condition for A’s making p true, but it is not a sufficient one; likewise for ‘Necessarily, if q then r’ and ‘r is true in virtue of q’.

If you believe all that, it’d be nice if one of truthmaking or in virtue of could be defined in terms of the other, so that we only have one primitive here rather than two. I think the prospects of defining truthmaking in terms of in virtue of are better than vice-versa, and I’d welcome thoughts on this.

How might one define the in virtue of relation that can hold between two true propositions in terms of the makes true relation that holds between a thing and a true proposition? Here are some of the obvious things that come to my mind, and why I don’t like them.

(1) p is true in virtue of q iff q makes p true

Okay, this one is obviously hopeless. For starters, if propositions are necessary existents, this entails that no contingent truth is true in virtue of anything. But even if propositions are contingent existents, presumably their existence is not contingent on them being true; they can exist and be false, and so this definition is still hopeless. Suppose 'X is wrong' is, as the consequentialist says, true in virtue of 'X has bad consequences'; the definition tells us that the latter proposition makes it true that X is wrong. But that proposition can exist and be false (X might have had good consequences), so now we’re committed to thinking that in a world where X has good consequences, X is still wrong, which is exactly the opposite of what the consequentialist wants.

(2) p is true in virtue of q iff the truth of q makes p true

This solves the above problem, but at the cost of admitting weird entities. What type of entity is the truth of q? A truth trope: the particularized truth of the proposition q? Nasty.

(3) p is true in virtue of q iff the state of affairs that q makes p true

That might be okay if there were a state of affairs that p for every true proposition p. But there’s not.

No: it’s no part of the definition of truthmaking that every truth has a truthmaker, and we should allow for the possibility that one proposition is true in virtue of another even though neither have truthmakers, as well as the possibility that two propositions lack truthmakers but where one is not true in virtue of the other. And if every truth does have a truthmaker, the definition will entail the wrong result that is true in virtue of any true negative existential, such as , since whatever makes the negative existential true necessarily makes it true that there is something, since everything that makes anything true necessarily makes it true that something exists, since it makes it true that it itself exists.

It doesn’t look to me like there’s a good way of defining in virtue of in terms of truthmaking; but I think truthmaking can be defined in terms of in virtue of. Truthmaker theory says that what is true is grounded in what there is: as I understand it, this is the claim that the totality of truths are ultimately true in virtue of just those truths that are concerned solely with ontology – that is, that any truth at all is ultimately true in virtue of some truth(s) concerning (solely) what there is.

Call the set containing all and only the brute propositions – that is, those that are not true in virtue of anything – BRUTUS. Consider also the set – call it EXISTS – of propositions whose entire content is that some thing, or some things, exist(s): call these propositions pure existence claims. (Pure existence claims will be expressible by sentences of the form ‘a exists’ or ‘the Xs exist’, where ‘a’ is a rigid designator and ‘the Xs’ a rigid plurally referring expression (i.e. it plurally refers in every possible world to the things that are actually the Xs if they exist, and it fails to refer if any of the actual Xs fail to exist.)

We can define truthmaking as follows.

(*) A proposition p is made true by X, or the Xs, just in case either (i) p belongs to BRUTUS & p belongs to EXISTS & p says that X (or the Xs) exist(s) or (ii) There is an x such that (p is true in virtue of x & x belongs to BRUTUS & x belongs to EXISTS & x says that X (or the Xs) exist(s)).

That is: a proposition is made true by some things, the Xs, if and only if it is the brutely true pure existence claim that the Xs exist or it is true in virtue of the brutely true pure existence claim that the Xs exist.

I’d welcome any thoughts on this. Especially if you think there’s a problem with the proposed definition of truthmaking in terms of in virtue of or if you think there’s a good way to define in virtue of in terms of truthmaking.

8 comments:

I'm not sure whether to call this a 'problem', but perhaps it's still worth noting: (*) is true, then the truthmaking relation isn't asymmetric.

Here's the thought. Many people (especially around here at Notre Dame) believe that propositions are 'ontologically basic'. I take it that they mean at least this much: if some proposition <p> exists, then the proposition <<p> exists> is true in virtue of no other propositions. (If you don't think that this could be the case, then you won't like what follows. But presumably, an analysis of what truthmaking consists in shouldn't rule it out.)

So, let <p> and <q> be two propositions; in particular, let <p> be the proposition <<q> exists> and let <q> be the proposition <<p> exists>. Then if <p> is 'ontologically basic' in at least the sense above, (*) classifies <q> as one of its truthmakers; similarly, (*) classifies <p> as a truthmaker for <q>. And so truthmaking isn't asymmetric. (If there are propositions that 'say of themselves' that they exist, then of course (*) implies that truthmaking also isn't irreflexive. I have no clue whether there are such things.)

Alex: that's a really interesting consequence I hadn't noticed - thanks! (I'm happy to consider it to be a feature rather than a bug unless anyone can convince me otherwise. . .)

Alexander: thanks for the reference. I had a look and McGrath doesn't quite seem to be defending my (1), although the position he defends is certainly similar in some ways. I'm glad you agree with me! Do you defend that anywhere?

I think the plausibility of your suggestion depends quite a lot on what kind of extension you think the IVO relation has. On some not-too-implausible views about its extension I can see scope for complaints. (Not that these couldn't be finessed, but they'd need some attention.)

For example, let p = /some philosopher exists/ and q = /Ross exists/, and suppose you want to say that p is true IVO q. (And you also want to say that Ross truthmakes q, which is in BRUTUS.) Then by your lights Ross truthmakes p too, right? But Ross's existence doesn't necessitate p, because in some worlds Ross exists without being a philosopher.

Carrie: yeah, but that just means that IVO-necessitarianism and TM-necessitarianism stand or fall together on my view, right? I'm happy with that. I mean, either thesis is debatable, but I'm not convinced we should have to make conceptual space for them coming apart (not that you said we should).

This might be slightly tangential to the main issue, but it was raised parenthetically in the first comment, so I'll just add that there does seem to be at least one proposition that should be counted as a truthmaker for itself. So the truthmaking relation turning out not to be irreflexive should be counted an advantage of a definition of truthmaking. The example I have in mind (which is from Marian David's "Truth-making and Correspondence" in Lowe & Rami's "Truth and Truth-making" anthology) is < There is at least one proposition >. I can't see any good reason for denying that this proposition makes itself true (of course, it has other truthmakers as well). If your definition of truthmaking allows this, then so much the better for the suggested definition. (Also, denying the irreflexivity of truthmaking could be helpful when it comes to providing truthmakers for formal truths as well - at any rate, it seems to give you more options).